Right Cauchy-Green tensor

In Equation (1.28) function M(t - r ) is the time-dependent memory function of linear viscoelasticity, non-dimensional scalars 4>i and 4>2 and are the functions of the first invariant of Q(t - f ) and F, t t ), which are, respectively, the right Cauchy Green tensor and its inverse (called the Finger strain tensor) (Mitsoulis, 1990). The memory function is usually expressed as... 

To hold the incompressibihty assumption the volume preserving part of the apphed deformation gradient needs to be utilized in the trial elastic part, with the left and right Cauchy-Green tensors given by [14]... 

The consideration of the assumed right Cauchy-Green tensor C +i = leads... 

C is referred to as the right Cauchy-Green tensor and B the left Cauchy-Green tensor. Then the deformation measure can be written as... 

Note 2.4 (Generalized strain measure (Hill 1978)9t). Since the right Cauchy-Green tensor C = is symmetric and the components are real numbers, there are three real eigenvalues that are set as A ( = 1,2,3) and the corresponding eigenvectors are given by Ni then we have... 

Note that the right Cauchy-Green tensor C and the Green strain E are not frame... 

Affinity at reaction stage r Acceleration Activity of species a Left Cauchy-Green tensor Body force per unit mass Diffusive body force Right Cauchy-Green tensor Mass-molar concentration Mass concentration of species a Mass-energy flux of the system... 

The right Cauchy-Green strain tensor corresponding to this deformation gradient is thus expressed as... 

Therein, Cs = FsFj and Jl,g = detFL, g are the right Cauchy-Green deformation tensor of the solid and the Jacobian of the gas and liquid phases respectively, where Fa denotes the deformation gradient of free energies and the specific entropies of the constituents [Pg.333]

Corresponding to U and V, two new tensors can be defined, which are used to calculate U and V. We have the right Cauchy-Green deformation tensor C and the left Cauchy-Green deformation tensor B ... 

Hence, the right-Cauchy-Green strain tensor reads as C(t)... 

In the large strain situation, we can split the deviatoric and volumetric terms 9] by redefining the deformation gradient tensor as F = Then, the right Cauchy-Green deformation tensor invariants become... 

In the above two equations, as well as in the rest of the equations in this section, subscripts 1, 2, and 3 indicate x, y, and z directions, respectively. The deformation tensor and its transpose can be combined to yield the right relative Cauchy-Green strain tensor, C, with components... 

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